Same content, different truth value
Kaplan, "Demonstratives", p.500:
[I]f I say, today,I was insulted yesterdayand you utter the same words tomorrow, what is said is different. If what we say differs in truth-value, that is enough to show that we say different things.
This criterion is frequently echoed. Here, for instance, is Lycan, Philosophy of Language, p.93:
...words on Twin Earth and the rest diverge in meaning from their counterparts on Earth. Of an Earth utterance and its Twin, one may be true and the other false; what more could be required for difference of meaning?
But the criterion strikes me as very implausible. Consider a possible world that differs from ours only by containing an extra isolated electron in some remote part of the universe, far outside our galaxy. When I say "the number of electrons is even", my utterance differs in truth value from the corresponding utterance of my twin at this world. Does it follow that we mean different things by "number" or "electron" or "even" (or "is")? No. The obvious explanation is rather that what both of us mean happens to be true in one world and false in the other.
In Kaplan's case, his criterion is also plainly inconsistent with his own theory of content. The sentence
S) All persons alive in 1977 will have died by 2077,
Kaplan claims, "expresses the same proposition no matter when said, by whom, or under what circumstances. The truth-value of that proposition may, of course, vary with possible circumstances, but the character is fixed" (p.506). This is correct on Kaplan's understanding of "proposition" and "character". But from the fact that (S) expresses the same proposition in every context it doesn't follow that it has the same truth value in every context. In a context at a world w where the age of people differs from the age of people in the actual world @, the utterance may have a different truth value than in a context at @, even though the proposition is the same: in both cases, it assigns, say, true to @ and false to w.
This is even more obvious for temporal and locational indices. Since English has temporal operators, contents must be both world- and time-dependent. Now consider the world-time pairs where
S2) it is raining in Berlin
is true. These are exactly the same pairs no matter when the sentence is uttered, by whom, or under what circumstances. So "it is raining in Berlin" (unlike "it is raining in Berlin now") has a fixed character for Kaplan. (Oddly, on p.504f., Kaplan wavers on this issue, but the claim is definitely built into the formal system introduced later.) Hence my present utterance of "it is raining in Berlin" expresses the same content as your utterance of "it is raining in Berlin" tomorrow. Yet the truth-value of our utterences may obviously differ.
Thus if what we say differs in truth-value, that is not enough to show that we say different things -- unless we say those things in exactly the same context.
(After having written this, I vaguely recall Frank Jackson (or was it David Chalmers?) making the same point somewhere. Anyway, it's worth spreading the word.)
To be fair to Kaplan, he surely means his criterion to apply within a world, not across worlds. Compare: if we have the same parents, we are siblings. That holds within a world, but not across possible worlds (two only children of the same parents in different possible worlds are not siblings).
It seems to me that Kaplan's criterion will be reasonable iff what one says is something (e.g. an eternal proposition) that has an absolute truth-value at a world. Maybe there are reasons to reject this assumption (e.g. if one takes what one says to be a time-indexed proposition, or something like a primary intension), and so to reject the criterion. But I think that takes more than considerations about other possible worlds.